Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#21779 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2308 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,5,10,6,9,18,24)(3,11,14,25,13,7,17,20)(4,8,15,23,16,22,29,32)(12,19,27,30,26,21,28,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,7)(4,12)(5,17)(6,13)(8,21)(9,11)(10,25)(14,18)(15,28)(16,26)(19,22)(20,24)(23,30)(27,29)(31,32);(1,4,6,16)(2,8,9,22)(3,12,13,26)(5,15,18,29)(7,19,11,21)(10,23,24,32)(14,27,17,28)(20,30,25,31);(2,9)(5,18)(7,11)(8,22)(14,17)(15,29)(19,21)(27,28)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14767);